Feature engineering for electricity load forecasting

The purpose of this notebook is to demonstrate how to use skrub and polars to perform feature engineering for electricity load forecasting.

We will build a set of features (and targets) from different data sources:

• Historical weather data for 10 medium to large urban areas in France;

• Holidays and standard calendar features for France;

• Historical electricity load data for the whole of France.

All these data sources cover a time range from March 23, 2021 to May 31, 2025.

Since our maximum forecasting horizon is 24 hours, we consider that the future weather data is known at a chosen prediction time. Similarly, the holidays and calendar features are known at prediction time for any point in the future.

Therefore, exogenous features derived from the weather and calendar data can be used to engineer “future covariates”. Since the load data is our prediction target, we will can also use it to engineer “past covariates” such as lagged features and rolling aggregations. The future values of the load data (with respect to the prediction time) are used as targets for the forecasting model.

Environment setup

We need to install some extra dependencies for this notebook if needed (when running jupyterlite). We need the development version of skrub to be able to use the skrub expressions.

%pip install -q https://pypi.anaconda.org/ogrisel/simple/polars/1.24.0/polars-1.24.0-cp39-abi3-emscripten_3_1_58_wasm32.whl
%pip install -q https://pypi.anaconda.org/ogrisel/simple/skrub/0.6.dev0/skrub-0.6.dev0-py3-none-any.whl
%pip install -q altair holidays plotly nbformat

ERROR: polars-1.24.0-cp39-abi3-emscripten_3_1_58_wasm32.whl is not a supported wheel on this platform.

Note: you may need to restart the kernel to use updated packages.

Note: you may need to restart the kernel to use updated packages.

Note: you may need to restart the kernel to use updated packages.

The following 3 imports are only needed to workaround some limitations when using polars in a pyodide/jupyterlite notebook.

TODO: remove those workarounds once pyodide 0.28 is released with support for the latest polars version.

import tzdata  # noqa: F401
import pandas as pd
from pyarrow.parquet import read_table

import altair
import numpy as np
import polars as pl
import skrub
from pathlib import Path
import holidays
import warnings

# Ignore warnings from pkg_resources triggered by Python 3.13's multiprocessing.
warnings.filterwarnings("ignore", category=UserWarning, module="pkg_resources")

Shared time range for all historical data sources

Let’s define a hourly time range from March 23, 2021 to May 31, 2025 that will be used to join the electricity load data and the weather data. The time range is in UTC timezone to avoid any ambiguity when joining with the weather data that is also in UTC.

We wrap the resulting polars dataframe in a skrub expression to benefit from the built-in skrub.TableReport display in the notebook. Using the skrub expression system will also be useful for other reasons: all operations in this notebook chain operations chained together in a directed acyclic graph that is automatically tracked by skrub. This allows us to extract the resulting pipeline and apply it to new data later on, exactly like a trained scikit-learn pipeline. The main difference is that we do so incrementally and while eagerly executing and inspecting the results of each step as is customary when working with dataframe libraries such as polars and pandas in Jupyter notebooks.

historical_data_start_time = skrub.var(
    "historical_data_start_time", pl.datetime(2021, 3, 23, hour=0, time_zone="UTC")
)
historical_data_end_time = skrub.var(
    "historical_data_end_time", pl.datetime(2025, 5, 31, hour=23, time_zone="UTC")
)

@skrub.deferred
def build_historical_time_range(
    historical_data_start_time,
    historical_data_end_time,
    time_interval="1h",
    time_zone="UTC",
):
    """Define an historical time range shared by all data sources."""
    return pl.DataFrame().with_columns(
        pl.datetime_range(
            start=historical_data_start_time,
            end=historical_data_end_time,
            time_zone=time_zone,
            interval=time_interval,
        ).alias("time"),
    )


time = build_historical_time_range(historical_data_start_time, historical_data_end_time)
time

<Call 'build_historical_time_range'>

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Result:

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If you run the above locally with pydot and graphviz installed, you can visualize the expression graph of the time variable by expanding the “Show graph” button.

Let’s now load the data records for the time range defined above.

To avoid network issues when running this notebook, the necessary data files have already been downloaded and saved in the datasets folder. See the README.md file for instructions to download the data manually if you want to re-run this notebook with more recent data.

data_source_folder = skrub.var("data_source_folder", Path("../datasets"))

for data_file in sorted(data_source_folder.skb.eval().iterdir()):
    print(data_file)

../datasets/README.md
../datasets/Total Load - Day Ahead _ Actual_202101010000-202201010000.csv
../datasets/Total Load - Day Ahead _ Actual_202201010000-202301010000.csv
../datasets/Total Load - Day Ahead _ Actual_202301010000-202401010000.csv
../datasets/Total Load - Day Ahead _ Actual_202401010000-202501010000.csv
../datasets/Total Load - Day Ahead _ Actual_202501010000-202601010000.csv
../datasets/weather_bayonne.parquet
../datasets/weather_brest.parquet
../datasets/weather_lille.parquet
../datasets/weather_limoges.parquet
../datasets/weather_lyon.parquet
../datasets/weather_marseille.parquet
../datasets/weather_nantes.parquet
../datasets/weather_paris.parquet
../datasets/weather_strasbourg.parquet
../datasets/weather_toulouse.parquet

We define a list of 10 medium to large urban areas to approximately cover most regions in France with a slight focus on most populated regions that are likely to drive electricity demand.

city_names = skrub.var(
    "city_names",
    [
        "paris",
        "lyon",
        "marseille",
        "toulouse",
        "lille",
        "limoges",
        "nantes",
        "strasbourg",
        "brest",
        "bayonne",
    ],
)


@skrub.deferred
def load_weather_data(time, city_names, data_source_folder):
    """Load and horizontal stack historical weather forecast data for each city."""
    all_city_weather = time
    for city_name in city_names:
        all_city_weather = all_city_weather.join(
            pl.from_arrow(
                read_table(f"{data_source_folder}/weather_{city_name}.parquet")
            )
            .with_columns([pl.col("time").dt.cast_time_unit("us")])
            .rename(lambda x: x if x == "time" else "weather_" + x + "_" + city_name),
            on="time",
        )
    return all_city_weather


all_city_weather = load_weather_data(time, city_names, data_source_folder)
all_city_weather

<Call 'load_weather_data'>

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Result:

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Calendar and holidays features

We leverage the holidays package to enrich the time range with some calendar features such as public holidays in France. We also add some features that are useful for time series forecasting such as the day of the week, the day of the year, and the hour of the day.

Note that the holidays package requires us to extract the date for the French timezone.

Similarly for the calendar features: all the time features are extracted from the time in the French timezone, since it is likely that electricity usage patterns are influenced by inhabitants’ daily routines aligned with the local timezone.

@skrub.deferred
def prepare_french_calendar_data(time):
    fr_time = pl.col("time").dt.convert_time_zone("Europe/Paris")
    fr_year_min = time.select(fr_time.dt.year().min()).item()
    fr_year_max = time.select(fr_time.dt.year().max()).item()
    holidays_fr = holidays.country_holidays(
        "FR", years=range(fr_year_min, fr_year_max + 1)
    )
    return time.with_columns(
        [
            fr_time.dt.hour().alias("cal_hour_of_day"),
            fr_time.dt.weekday().alias("cal_day_of_week"),
            fr_time.dt.ordinal_day().alias("cal_day_of_year"),
            fr_time.dt.year().alias("cal_year"),
            fr_time.dt.date().is_in(holidays_fr.keys()).alias("cal_is_holiday"),
        ],
    )


calendar = prepare_french_calendar_data(time)
calendar

<Call 'prepare_french_calendar_data'>

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Result:

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Electricity load data

Finally we load the electricity load data. This data will both be used as a target variable but also to craft some lagged and window-aggregated features.

@skrub.deferred
def load_electricity_load_data(time, data_source_folder):
    """Load and aggregate historical load data from the raw CSV files."""
    load_data_files = [
        data_file
        for data_file in sorted(data_source_folder.iterdir())
        if data_file.name.startswith("Total Load - Day Ahead")
        and data_file.name.endswith(".csv")
    ]
    return time.join(
        (
            pl.concat(
                [
                    pl.from_pandas(pd.read_csv(data_file, na_values=["N/A", "-"])).drop(
                        ["Day-ahead Total Load Forecast [MW] - BZN|FR"]
                    )
                    for data_file in load_data_files
                ]
            ).select(
                [
                    pl.col("Time (UTC)")
                    .str.split(by=" - ")
                    .list.first()
                    .str.to_datetime("%d.%m.%Y %H:%M", time_zone="UTC")
                    .alias("time"),
                    pl.col("Actual Total Load [MW] - BZN|FR").alias("load_mw"),
                ]
            )
        ),
        on="time",
    )


electricity = load_electricity_load_data(time, data_source_folder)
electricity

<Call 'load_electricity_load_data'>

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electricity.filter(pl.col("load_mw").is_null())

<CallMethod 'filter'>

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electricity.filter(
    (pl.col("time") > pl.datetime(2021, 10, 30, hour=10, time_zone="UTC"))
    & (pl.col("time") < pl.datetime(2021, 10, 31, hour=10, time_zone="UTC"))
).skb.eval().plot.line(x="time:T", y="load_mw:Q")

electricity = electricity.with_columns([pl.col("load_mw").interpolate()])
electricity.filter(
    (pl.col("time") > pl.datetime(2021, 10, 30, hour=10, time_zone="UTC"))
    & (pl.col("time") < pl.datetime(2021, 10, 31, hour=10, time_zone="UTC"))
).skb.eval().plot.line(x="time:T", y="load_mw:Q")

Lagged features

We can now create some lagged features from the electricity load data.

We will create 3 hourly lagged features, 1 daily lagged feature, and 1 weekly lagged feature. We will also create a rolling median and inter-quartile feature over the last 24 hours and over the last 7 days.

def iqr(col, *, window_size: int):
    """Inter-quartile range (IQR) of a column."""
    return col.rolling_quantile(0.75, window_size=window_size) - col.rolling_quantile(
        0.25, window_size=window_size
    )


electricity_lagged = electricity.with_columns(
    [pl.col("load_mw").shift(i).alias(f"load_mw_lag_{i}h") for i in range(1, 4)]
    + [
        pl.col("load_mw").shift(24).alias("load_mw_lag_1d"),
        pl.col("load_mw").shift(24 * 7).alias("load_mw_lag_1w"),
        pl.col("load_mw")
        .rolling_median(window_size=24)
        .alias("load_mw_rolling_median_24h"),
        pl.col("load_mw")
        .rolling_median(window_size=24 * 7)
        .alias("load_mw_rolling_median_7d"),
        iqr(pl.col("load_mw"), window_size=24).alias("load_mw_iqr_24h"),
        iqr(pl.col("load_mw"), window_size=24 * 7).alias("load_mw_iqr_7d"),
    ],
)
electricity_lagged

<CallMethod 'with_columns'>

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Result:

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altair.Chart(electricity_lagged.tail(100).skb.eval()).transform_fold(
    [
        "load_mw",
        "load_mw_lag_1h",
        "load_mw_lag_2h",
        "load_mw_lag_3h",
        "load_mw_lag_1d",
        "load_mw_lag_1w",
        "load_mw_rolling_median_24h",
        "load_mw_rolling_median_7d",
        "load_mw_rolling_iqr_24h",
        "load_mw_rolling_iqr_7d",
    ],
    as_=["key", "load_mw"],
).mark_line(tooltip=True).encode(x="time:T", y="load_mw:Q", color="key:N").interactive()

Remark lagged features engineering and system lag

When working with historical data, we often have access to all the past measurements in the dataset. However, when we want to use the lagged features in a forecasting model, we need to be careful about the length of the system lag: the time between a timestamped measurement is made in the real world and the time the record is made available to the downstream application (in our case, a deployed predictive pipeline).

System lag is rarely explicitly represented in the data sources even if such delay can be as large as several hours or even days and can sometimes be irregular. For instance, if there is a human intervention in the data recording process, holidays and weekends can punctually add significant delay.

If the system lag is larger than the maximum feature engineering lag, the resulting features be filled with missing values once deployed. More importantly, if the system lag is not handled explicitly, those resulting missing values will only be present in the features computed for the deployed system but not present in the features computed to train and backtest the system before deployment.

This structural discrepancy can severely degrade the performance of the deployed model compared to the performance estimated from backtesting on the historical data.

We will set this problem aside for now but discuss it again in a later section of this tutorial.

Investigating outliers in the lagged features

Let’s use the skrub.TableReport tool to look at the plots of the marginal distribution of the lagged features.

from skrub import TableReport

TableReport(electricity_lagged.skb.eval())

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Let’s extract the dates where the inter-quartile range of the load is greater than 15,000 MW.

electricity_lagged.filter(pl.col("load_mw_iqr_7d") > 15_000)[
    "time"
].dt.date().unique().sort().to_list().skb.eval()

[datetime.date(2021, 12, 26),
 datetime.date(2021, 12, 27),
 datetime.date(2021, 12, 28),
 datetime.date(2022, 1, 7),
 datetime.date(2022, 1, 8),
 datetime.date(2023, 1, 19),
 datetime.date(2023, 1, 20),
 datetime.date(2023, 1, 21),
 datetime.date(2024, 1, 10),
 datetime.date(2024, 1, 11),
 datetime.date(2024, 1, 12),
 datetime.date(2024, 1, 13)]

We observe 3 date ranges with high inter-quartile range. Let’s plot the electricity load and the lagged features for the first data range along with the weather data for Paris.

altair.Chart(
    electricity_lagged.filter(
        (pl.col("time") > pl.datetime(2021, 12, 1, time_zone="UTC"))
        & (pl.col("time") < pl.datetime(2021, 12, 31, time_zone="UTC"))
    ).skb.eval()
).transform_fold(
    [
        "load_mw",
        "load_mw_iqr_7d",
    ],
).mark_line(
    tooltip=True
).encode(
    x="time:T", y="value:Q", color="key:N"
).interactive()

altair.Chart(
    all_city_weather.filter(
        (pl.col("time") > pl.datetime(2021, 12, 1, time_zone="UTC"))
        & (pl.col("time") < pl.datetime(2021, 12, 31, time_zone="UTC"))
    ).skb.eval()
).transform_fold(
    [f"weather_temperature_2m_{city_name}" for city_name in city_names.skb.eval()],
).mark_line(
    tooltip=True
).encode(
    x="time:T", y="value:Q", color="key:N"
).interactive()

Based on the plots above, we can see that the electricity load was high just before the Christmas holidays due to low temperatures. Then the load suddenly dropped because temperatures went higher right at the start of the end-of-year holidays.

So those outliers do not seem to be caused to a data quality issue but rather due to a real change in the electricity load demand. We could conduct similar analysis for the other date ranges with high inter-quartile range but we will skip that for now.

If we had observed significant data quality issues over extended periods of time could have been addressed by removing the corresponding rows from the dataset. However, this would make the lagged and windowing feature engineering challenging to reimplement correctly. A better approach would be to keep a contiguous dataset assign 0 weights to the affected rows when fitting or evaluating the trained models via the use of the sample_weight parameter.

Final dataset

We now assemble the dataset that will be used to train and evaluate the forecasting models via backtesting.

prediction_start_time = skrub.var(
    "prediction_start_time", historical_data_start_time.skb.eval() + pl.duration(days=7)
)
prediction_end_time = skrub.var(
    "prediction_end_time", historical_data_end_time.skb.eval() - pl.duration(hours=24)
)


@skrub.deferred
def define_prediction_time_range(prediction_start_time, prediction_end_time):
    return pl.DataFrame().with_columns(
        pl.datetime_range(
            start=prediction_start_time,
            end=prediction_end_time,
            time_zone="UTC",
            interval="1h",
        ).alias("prediction_time"),
    )


prediction_time = define_prediction_time_range(
    prediction_start_time, prediction_end_time
)
prediction_time

<Call 'define_prediction_time_range'>

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@skrub.deferred
def build_features(
    prediction_time,
    electricity_lagged,
    all_city_weather,
    calendar,
    future_feature_horizons=[1, 24],
):

    return (
        prediction_time.join(
            electricity_lagged, left_on="prediction_time", right_on="time"
        )
        .join(
            all_city_weather.select(
                [pl.col("time")]
                + [
                    pl.col(c).shift(-h).alias(c + f"_future_{h}h")
                    for c in all_city_weather.columns
                    if c != "time"
                    for h in future_feature_horizons
                ]
            ),
            left_on="prediction_time",
            right_on="time",
        )
        .join(
            calendar.select(
                [pl.col("time")]
                + [
                    pl.col(c).shift(-h).alias(c + f"_future_{h}h")
                    for c in calendar.columns
                    if c != "time"
                    for h in future_feature_horizons
                ]
            ),
            left_on="prediction_time",
            right_on="time",
        )
    ).drop("prediction_time")


features = build_features(
    prediction_time=prediction_time,
    electricity_lagged=electricity_lagged,
    all_city_weather=all_city_weather,
    calendar=calendar,
).skb.mark_as_X()

features

<Call 'build_features'>

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Let’s build training and evaluation targets for all possible horizons from 1 to 24 hours.

horizons = range(1, 25)
target_column_name_pattern = "load_mw_horizon_{horizon}h"


@skrub.deferred
def build_targets(prediction_time, electricity, horizons):
    return prediction_time.join(
        electricity.with_columns(
            [
                pl.col("load_mw")
                .shift(-h)
                .alias(target_column_name_pattern.format(horizon=h))
                for h in horizons
            ]
        ),
        left_on="prediction_time",
        right_on="time",
    )


targets = build_targets(prediction_time, electricity, horizons)
targets

<Call 'build_targets'>

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For now, let’s focus on the last horizon (24 hours) to train a model predicting the electricity load at the next 24 hours.

horizon_of_interest = horizons[-1]  # Focus on the 24-hour horizon
target_column_name = target_column_name_pattern.format(horizon=horizon_of_interest)
predicted_target_column_name = "predicted_" + target_column_name
target = targets[target_column_name].skb.mark_as_y()
target

<GetItem 'load_mw_horizon_24h'>

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Let’s define our first single output prediction pipeline. This pipeline chains our previous feature engineering steps with a skrub.DropCols step to drop some columns that we do not want to use as features, and a HistGradientBoostingRegressor model from scikit-learn.

The skrub.choose_from, skrub.choose_float, and skrub.choose_int functions are used to define hyperparameters that can be tuned via cross-validated randomized search.

from sklearn.ensemble import HistGradientBoostingRegressor
import skrub.selectors as s


features_with_dropped_cols = features.skb.apply(
    skrub.DropCols(
        cols=skrub.choose_from(
            {
                "none": s.glob(""),  # No column has an empty name.
                "load": s.glob("load_*"),
                "rolling_load": s.glob("load_mw_rolling_*"),
                "weather": s.glob("weather_*"),
                "temperature": s.glob("weather_temperature_*"),
                "moisture": s.glob("weather_moisture_*"),
                "cloud_cover": s.glob("weather_cloud_cover_*"),
                "calendar": s.glob("cal_*"),
                "holiday": s.glob("cal_is_holiday*"),
                "future_1h": s.glob("*_future_1h"),
                "future_24h": s.glob("*_future_24h"),
                "non_paris_weather": s.glob("weather_*") & ~s.glob("weather_*_paris_*"),
            },
            name="dropped_cols",
        )
    )
)

hgbr_predictions = features_with_dropped_cols.skb.apply(
    HistGradientBoostingRegressor(
        random_state=0,
        loss=skrub.choose_from(["squared_error", "poisson", "gamma"], name="loss"),
        learning_rate=skrub.choose_float(
            0.01, 1, default=0.1, log=True, name="learning_rate"
        ),
        max_leaf_nodes=skrub.choose_int(
            3, 300, default=30, log=True, name="max_leaf_nodes"
        ),
    ),
    y=target,
)
hgbr_predictions

<Apply HistGradientBoostingRegressor>

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The predictions expression captures the whole expression graph that includes the feature engineering steps, the target variable, and the model training step.

In particular, the input data keys for the full pipeline can be inspected as follows:

hgbr_predictions.skb.get_data().keys()

dict_keys(['prediction_start_time', 'prediction_end_time', 'historical_data_start_time', 'historical_data_end_time', 'data_source_folder', 'city_names'])

Furthermore, the hyper-parameters of the full pipeline can be retrieved as follows:

hgbr_pipeline = hgbr_predictions.skb.get_pipeline()
hgbr_pipeline.describe_params()

{'dropped_cols': 'none',
 'learning_rate': 0.1,
 'loss': 'squared_error',
 'max_leaf_nodes': 30}

When running this notebook locally, you can also interactively inspect all the steps of the DAG using the following (once uncommented):

# predictions.skb.full_report()

Since we passed input values to all the upstream skrub variables, skrub automatically evaluates the whole expression graph graph (train and predict on the same data) so that we can interactively check that everything will work as expected.

Let’s use altair to visualize the predictions against the target values for the last 24 hours of the prediction time range used to train the model. This allows us can (over)fit the data with the features at hand.

altair.Chart(
    pl.concat(
        [
            targets.skb.eval(),
            hgbr_predictions.rename(
                {target_column_name: predicted_target_column_name}
            ).skb.eval(),
        ],
        how="horizontal",
    ).tail(24 * 7)
).transform_fold(
    [target_column_name, predicted_target_column_name],
).mark_line(
    tooltip=True
).encode(
    x="prediction_time:T", y="value:Q", color="key:N"
).interactive()

Assessing the model performance via cross-validation

Being able to fit the training data is not enough. We need to assess the ability of the training pipeline to learn a predictive model that can generalize to unseen data.

Furthermore, we want to assess the uncertainty of this estimate of the generalization performance via time-based cross-validation, also known as backtesting.

from sklearn.model_selection import TimeSeriesSplit


max_train_size = 2 * 52 * 24 * 7  # max ~2 years of training data
test_size = 24 * 7 * 24  # 24 weeks of test data
gap = 7 * 24  # 1 week gap between train and test sets
ts_cv_5 = TimeSeriesSplit(
    n_splits=5, max_train_size=max_train_size, test_size=test_size, gap=gap
)

for fold_idx, (train_idx, test_idx) in enumerate(
    ts_cv_5.split(prediction_time.skb.eval())
):
    print(f"CV iteration #{fold_idx}")
    train_datetimes = prediction_time.skb.eval()[train_idx]
    test_datetimes = prediction_time.skb.eval()[test_idx]
    print(
        f"Train: {train_datetimes.shape[0]} rows, "
        f"Test: {test_datetimes.shape[0]} rows"
    )
    print(f"Train time range: {train_datetimes[0, 0]} to " f"{train_datetimes[-1, 0]} ")
    print(f"Test time range: {test_datetimes[0, 0]} to " f"{test_datetimes[-1, 0]} ")
    print()

CV iteration #0
Train: 16224 rows, Test: 4032 rows
Train time range: 2021-03-30 00:00:00+00:00 to 2023-02-03 23:00:00+00:00 
Test time range: 2023-02-11 00:00:00+00:00 to 2023-07-28 23:00:00+00:00 

CV iteration #1
Train: 17472 rows, Test: 4032 rows
Train time range: 2021-07-24 00:00:00+00:00 to 2023-07-21 23:00:00+00:00 
Test time range: 2023-07-29 00:00:00+00:00 to 2024-01-12 23:00:00+00:00 

CV iteration #2
Train: 17472 rows, Test: 4032 rows
Train time range: 2022-01-08 00:00:00+00:00 to 2024-01-05 23:00:00+00:00 
Test time range: 2024-01-13 00:00:00+00:00 to 2024-06-28 23:00:00+00:00 

CV iteration #3
Train: 17472 rows, Test: 4032 rows
Train time range: 2022-06-25 00:00:00+00:00 to 2024-06-21 23:00:00+00:00 
Test time range: 2024-06-29 00:00:00+00:00 to 2024-12-13 23:00:00+00:00 

CV iteration #4
Train: 17472 rows, Test: 4032 rows
Train time range: 2022-12-10 00:00:00+00:00 to 2024-12-06 23:00:00+00:00 
Test time range: 2024-12-14 00:00:00+00:00 to 2025-05-30 23:00:00+00:00 

from sklearn.metrics import make_scorer, mean_absolute_percentage_error, get_scorer
from sklearn.metrics import d2_tweedie_score


cv_results = hgbr_predictions.skb.cross_validate(
    cv=ts_cv_5,
    scoring={
        "mape": make_scorer(mean_absolute_percentage_error),
        "r2": get_scorer("r2"),
        "d2_poisson": make_scorer(d2_tweedie_score, power=1.0),
        "d2_gamma": make_scorer(d2_tweedie_score, power=2.0),
    },
    return_train_score=True,
    return_pipeline=True,
    verbose=1,
    n_jobs=-1,
)
cv_results.round(3)

[Parallel(n_jobs=-1)]: Using backend LokyBackend with 4 concurrent workers.

[Parallel(n_jobs=-1)]: Done   5 out of   5 | elapsed:    8.4s finished

	fit_time	score_time	test_mape	train_mape	test_r2	train_r2	test_d2_poisson	train_d2_poisson	test_d2_gamma	train_d2_gamma	pipeline
0	2.936	0.060	0.027	0.012	0.963	0.994	0.962	0.994	0.961	0.994	SkrubPipeline(expr=<Apply HistGradientBoosting...
1	3.229	0.063	0.024	0.013	0.978	0.994	0.977	0.994	0.976	0.993	SkrubPipeline(expr=<Apply HistGradientBoosting...
2	3.242	0.060	0.023	0.014	0.974	0.993	0.974	0.993	0.975	0.992	SkrubPipeline(expr=<Apply HistGradientBoosting...
3	3.207	0.061	0.019	0.014	0.980	0.993	0.980	0.992	0.980	0.992	SkrubPipeline(expr=<Apply HistGradientBoosting...
4	2.154	0.037	0.023	0.014	0.977	0.993	0.978	0.992	0.978	0.992	SkrubPipeline(expr=<Apply HistGradientBoosting...

def collect_cv_predictions(pipelines, cv_splitter, predictions, prediction_time):
    index_generator = cv_splitter.split(prediction_time.skb.eval())

    def splitter(X, y, index_generator):
        """Workaround to transform a scikit-learn splitter into a function understood
        by `skrub.train_test_split`."""
        train_idx, test_idx = next(index_generator)
        return X[train_idx], X[test_idx], y[train_idx], y[test_idx]

    results = []
    for (_, test_idx), pipeline in zip(
        cv_splitter.split(prediction_time.skb.eval()), pipelines
    ):
        split = predictions.skb.train_test_split(
            predictions.skb.get_data(),
            splitter=splitter,
            index_generator=index_generator,
        )
        results.append(
            pl.DataFrame(
                {
                    "prediction_time": prediction_time.skb.eval()[test_idx],
                    "load_mw": split["y_test"],
                    "predicted_load_mw": pipeline.predict(split["test"]),
                }
            )
        )
    return results

cv_predictions = collect_cv_predictions(
    cv_results["pipeline"], ts_cv_5, hgbr_predictions, prediction_time
)
cv_predictions[0]

shape: (4_032, 3)

prediction_time	load_mw	predicted_load_mw
datetime[μs, UTC]	f64	f64
2023-02-11 00:00:00 UTC	59258.0	59855.334418
2023-02-11 01:00:00 UTC	58654.0	59958.654564
2023-02-11 02:00:00 UTC	56155.0	57666.184522
2023-02-11 03:00:00 UTC	54463.0	55832.880673
2023-02-11 04:00:00 UTC	54698.0	57121.984097
…	…	…
2023-07-28 19:00:00 UTC	38781.0	40093.987086
2023-07-28 20:00:00 UTC	38455.0	39343.771368
2023-07-28 21:00:00 UTC	39972.0	40738.151594
2023-07-28 22:00:00 UTC	39825.0	39449.468131
2023-07-28 23:00:00 UTC	36822.0	35828.293662

def lorenz_curve(observed_value, predicted_value, n_samples=1_000):
    """Compute the Lorenz curve for a given true and predicted values."""

    def gini_index(cum_proportion_population, cum_proportion_y_true):
        from sklearn.metrics import auc

        return 1 - 2 * auc(cum_proportion_population, cum_proportion_y_true)

    observed_value = np.asarray(observed_value)
    predicted_value = np.asarray(predicted_value)

    sort_idx = np.argsort(predicted_value)
    observed_value_sorted = observed_value[sort_idx]

    original_n_samples = observed_value_sorted.shape[0]
    cum_proportion_population = np.cumsum(np.ones(original_n_samples))
    cum_proportion_population /= cum_proportion_population[-1]

    cum_proportion_y_true = np.cumsum(observed_value_sorted)
    cum_proportion_y_true /= cum_proportion_y_true[-1]

    gini_model = gini_index(cum_proportion_population, cum_proportion_y_true)

    cum_proportion_population_interpolated = np.linspace(0, 1, n_samples)
    cum_proportion_y_true_interpolated = np.interp(
        cum_proportion_population_interpolated,
        cum_proportion_population,
        cum_proportion_y_true,
    )

    return pl.DataFrame(
        {
            "cum_population": cum_proportion_population_interpolated,
            "cum_observed": cum_proportion_y_true_interpolated,
        }
    ).with_columns(
        pl.lit(gini_model).alias("gini_index"),
    )


def plot_lorenz_curve(cv_predictions, n_samples=1_000):
    """Plot the Lorenz curve for a given true and predicted values."""

    results = []
    for fold_idx, predictions in enumerate(cv_predictions):
        results.append(
            lorenz_curve(
                observed_value=predictions["load_mw"],
                predicted_value=predictions["predicted_load_mw"],
                n_samples=n_samples,
            ).with_columns(
                pl.lit(fold_idx).alias("fold_idx"),
                pl.lit("Model").alias("model"),
            )
        )

        results.append(
            lorenz_curve(
                observed_value=predictions["load_mw"],
                predicted_value=predictions["load_mw"],
                n_samples=n_samples,
            ).with_columns(
                pl.lit(fold_idx).alias("fold_idx"),
                pl.lit("Oracle").alias("model"),
            )
        )

    results = pl.concat(results)

    gini_stats = results.group_by("model").agg(
        [
            pl.col("gini_index")
            .mean()
            .map_elements(lambda x: f"{x:.4f}", return_dtype=pl.String)
            .alias("gini_mean"),
            pl.col("gini_index")
            .std()
            .map_elements(lambda x: f"{x:.4f}", return_dtype=pl.String)
            .alias("gini_std_dev"),
        ]
    )

    results = results.join(gini_stats, on="model").with_columns(
        pl.format("{} (Gini: {} +/- {})", "model", "gini_mean", "gini_std_dev").alias(
            "model_label"
        )
    )

    model_chart = (
        altair.Chart(results)
        .mark_line(strokeDash=[4, 2, 4, 2], opacity=0.8, tooltip=True)
        .encode(
            x=altair.X(
                "cum_population:Q",
                title="Fraction of observations sorted by predicted label",
            ),
            y=altair.Y("cum_observed:Q", title="Cumulative observed load proportion"),
            color=altair.Color(
                "model_label:N", legend=altair.Legend(title="Models"), sort=None
            ),
            detail="fold_idx:N",
        )
    )

    diagonal_chart = (
        altair.Chart(
            pl.DataFrame(
                {
                    "cum_population": [0, 1],
                    "cum_observed": [0, 1],
                    "model_label": "Non-informative model (Gini = 0.0)",
                }
            )
        )
        .mark_line(strokeDash=[4, 4], opacity=0.5, tooltip=True)
        .encode(
            x=altair.X(
                "cum_population:Q",
                title="Fraction of observations sorted by predicted label",
            ),
            y=altair.Y("cum_observed:Q", title="Cumulative observed load proportion"),
            color=altair.Color(
                "model_label:N", legend=altair.Legend(title="Models"), sort=None
            ),
        )
    )

    return model_chart + diagonal_chart


plot_lorenz_curve(cv_predictions, n_samples=500).interactive()

def plot_reliability_diagram(
    cv_predictions, kind="mean", quantile_level=0.5, n_bins=10
):
    # min and max load over all predictions and observations for any folds:
    all_loads = pl.concat(
        [
            cv_prediction.select(["load_mw", "predicted_load_mw"])
            for cv_prediction in cv_predictions
        ]
    )
    all_loads = pl.concat(all_loads["load_mw", "predicted_load_mw"])
    min_load, max_load = all_loads.min(), all_loads.max()
    scale = altair.Scale(domain=[min_load, max_load])

    # Create the perfect line
    chart = (
        altair.Chart(
            pl.DataFrame(
                {
                    "mean_predicted_load_mw": [min_load, max_load],
                    "mean_load_mw": [min_load, max_load],
                    "label": ["Perfect"] * 2,
                }
            )
        )
        .mark_line(tooltip=True, opacity=0.8, strokeDash=[5, 5])
        .encode(
            x=altair.X("mean_predicted_load_mw:Q", scale=scale),
            y=altair.Y("mean_load_mw:Q", scale=scale),
            color=altair.Color(
                "label:N",
                scale=altair.Scale(range=["black"]),
                legend=altair.Legend(title="Legend"),
            ),
        )
    )

    # Add lines for each CV fold with date labels
    for fold_idx, cv_predictions_i in enumerate(cv_predictions):
        # Get date range for this CV fold
        min_date = cv_predictions_i["prediction_time"].min().strftime("%Y-%m-%d")
        max_date = cv_predictions_i["prediction_time"].max().strftime("%Y-%m-%d")
        fold_label = f"#{fold_idx} - {min_date} to {max_date}"

        if kind == "mean":
            y_name = "mean_load_mw"
            agg_expr = pl.col("load_mw")
        elif kind == "quantile":
            y_name = "quantile_of_load_mw"
            agg_expr = (
                pl.col("load_mw").quantile(quantile_level)
            )
        else:
            raise ValueError(f"Unknown kind: {kind}. Use 'mean' or 'quantile'.")

        mean_per_bins = (
            cv_predictions_i.group_by(
                pl.col("predicted_load_mw").qcut(np.linspace(0, 1, n_bins))
            )
            .agg(
                [
                    agg_expr.alias(y_name),
                    pl.col("predicted_load_mw").mean().alias("mean_predicted_load_mw"),
                ]
            )
            .sort("predicted_load_mw")
            .with_columns(pl.lit(fold_label).alias("fold_label"))
        )

        chart += (
            altair.Chart(mean_per_bins)
            .mark_line(tooltip=True, point=True, opacity=0.8)
            .encode(
                x=altair.X("mean_predicted_load_mw:Q", scale=scale),
                y=altair.Y(f"{y_name}:Q", scale=scale),
                color=altair.Color(
                    "fold_label:N",
                    legend=altair.Legend(title=None),
                ),
                detail=altair.Detail("fold_label:N"),
            )
        )
    return chart.resolve_scale(color="independent")


plot_reliability_diagram(cv_predictions).interactive().properties(
    title="Reliability diagram from cross-validation predictions"
)

def plot_residuals_vs_predicted(cv_predictions):
    """Plot residuals vs predicted values scatter plot for all CV folds."""
    all_scatter_plots = []

    x_title = "Predicted Load (MW)"
    y_title = "Residual load (MW): predicted - actual"

    for i, cv_prediction in enumerate(cv_predictions):
        # Get date range for this CV fold
        min_date = cv_prediction["prediction_time"].min().strftime("%Y-%m-%d")
        max_date = cv_prediction["prediction_time"].max().strftime("%Y-%m-%d")
        fold_label = f"#{i+1} - {min_date} to {max_date}"

        # Calculate residuals
        residuals_data = cv_prediction.with_columns(
            [(pl.col("predicted_load_mw") - pl.col("load_mw")).alias("residual")]
        ).with_columns([pl.lit(fold_label).alias("fold_label")])

        # Create scatter plot for this CV fold
        scatter_plot = (
            altair.Chart(residuals_data)
            .mark_circle(opacity=0.6, size=20)
            .encode(
                x=altair.X(
                    "predicted_load_mw:Q",
                    title=x_title,
                    scale=altair.Scale(zero=False),
                ),
                y=altair.Y("residual:Q", title=y_title),
                color=altair.Color("fold_label:N", legend=None),
                tooltip=[
                    "prediction_time:T",
                    "load_mw:Q",
                    "predicted_load_mw:Q",
                    "residual:Q",
                    "fold_label:N",
                ],
            )
        )

        all_scatter_plots.append(scatter_plot)

    # Get the range of predicted values for the perfect line
    all_predictions = pl.concat(
        [cv_pred["predicted_load_mw"] for cv_pred in cv_predictions]
    )
    min_pred, max_pred = all_predictions.min(), all_predictions.max()

    # Create perfect residuals line at y=0
    perfect_line = (
        altair.Chart(
            pl.DataFrame(
                {
                    "predicted_load_mw": [min_pred, max_pred],
                    "perfect_residual": [0, 0],
                    "label": ["Perfect"] * 2,
                }
            )
        )
        .mark_line(strokeDash=[5, 5], opacity=0.8, color="black")
        .encode(
            x=altair.X("predicted_load_mw:Q", title=x_title),
            y=altair.Y("perfect_residual:Q", title=y_title),
            color=altair.Color(
                "label:N",
                scale=altair.Scale(range=["black"]),
                legend=None,
            ),
        )
    )
    # Combine all scatter plots
    combined_scatter = all_scatter_plots[0]
    for plot in all_scatter_plots[1:]:
        combined_scatter += plot

    # Layer the scatter plots with the perfect line
    return (combined_scatter + perfect_line).resolve_scale(color="independent")


plot_residuals_vs_predicted(cv_predictions).interactive().properties(
    title="Residuals vs Predicted Values from cross-validation predictions"
)

def plot_binned_residuals(cv_predictions, by="hour"):
    """Plot the average residuals binned by time period, one line per CV fold."""
    # Configure binning based on the 'by' parameter
    if by == "hour":
        time_column = "hour_of_day"
        time_extractor = pl.col("prediction_time").dt.hour().alias(time_column)
        x_title = "Hour of day"
    elif by == "month":
        time_column = "month_of_year"
        time_extractor = pl.col("prediction_time").dt.month().alias(time_column)
        x_title = "Month of year"
    else:
        raise ValueError(f"Unsupported binning method: {by}. Use 'hour' or 'month'.")

    all_iqr_bands = []
    all_mean_lines = []
    time_range = None  # Will store the min/max time values for the perfect line

    for i, cv_prediction in enumerate(cv_predictions):
        # Get date range for this CV fold
        min_date = cv_prediction["prediction_time"].min().strftime("%Y-%m-%d")
        max_date = cv_prediction["prediction_time"].max().strftime("%Y-%m-%d")
        fold_label = f"#{i+1} - {min_date} to {max_date}"

        # Create residuals and time binning columns
        residuals_detailed = cv_prediction.with_columns(
            [
                (pl.col("predicted_load_mw") - pl.col("load_mw")).alias("residual"),
                time_extractor,
            ]
        )

        # Calculate statistics for this CV fold
        residuals_stats = (
            residuals_detailed.group_by(time_column)
            .agg(
                [
                    pl.col("residual").mean().round(1).alias("mean_residual"),
                    pl.col("residual").quantile(0.25).round(1).alias("q25_residual"),
                    pl.col("residual").quantile(0.75).round(1).alias("q75_residual"),
                ]
            )
            .sort(time_column)
            .with_columns(pl.lit(fold_label).alias("fold_label"))
        )

        # Store time range for perfect line (use the first CV fold)
        if time_range is None:
            time_range = (
                residuals_stats[time_column].min(),
                residuals_stats[time_column].max(),
            )
        else:
            time_range = (
                min(time_range[0], residuals_stats[time_column].min()),
                max(time_range[1], residuals_stats[time_column].max()),
            )
        # Create IQR band for this CV fold
        iqr_band = (
            altair.Chart(residuals_stats)
            .mark_area(opacity=0.15)
            .encode(
                x=altair.X(f"{time_column}:O", title=x_title),
                y=altair.Y("q25_residual:Q"),
                y2=altair.Y2("q75_residual:Q"),
            )
        )

        # Create mean line for this CV fold
        mean_line = (
            altair.Chart(residuals_stats)
            .mark_line(tooltip=True, point=True, opacity=0.8)
            .encode(
                x=altair.X(f"{time_column}:O", title=x_title),
                y=altair.Y("mean_residual:Q", title="Mean residual (MW)"),
                color=altair.Color("fold_label:N", legend=None),
                detail="fold_label:N",
            )
        )

        all_iqr_bands.append(iqr_band)
        all_mean_lines.append(mean_line)

    # Create perfect residuals line at y=0
    perfect_line = (
        altair.Chart(
            pl.DataFrame(
                {
                    time_column: [time_range[0], time_range[1]],
                    "perfect_residual": [0, 0],
                    "label": ["Perfect"] * 2,
                }
            )
        )
        .mark_line(strokeDash=[5, 5], opacity=0.8, color="black")
        .encode(
            x=altair.X(f"{time_column}:O", title=x_title),
            y=altair.Y("perfect_residual:Q", title="Mean residual (MW)"),
            color=altair.Color(
                "label:N",
                scale=altair.Scale(range=["black"]),
                legend=None,
            ),
        )
    )

    # Combine all IQR bands
    combined_iqr = all_iqr_bands[0]
    for band in all_iqr_bands[1:]:
        combined_iqr += band

    # Combine all mean lines
    combined_lines = all_mean_lines[0]
    for line in all_mean_lines[1:]:
        combined_lines += line

    # Layer the IQR bands behind the mean lines, with perfect line on top
    return (combined_iqr + combined_lines + perfect_line).resolve_scale(
        color="independent"
    )


plot_binned_residuals(cv_predictions, by="hour").interactive().properties(
    title="Residuals by hour of the day from cross-validation predictions"
)

plot_binned_residuals(cv_predictions, by="month").interactive().properties(
    title="Residuals by hour of the day from cross-validation predictions"
)

ts_cv_2 = TimeSeriesSplit(
    n_splits=2, test_size=test_size, max_train_size=max_train_size, gap=24
)
randomized_search_ridge = hgbr_predictions.skb.get_randomized_search(
    cv=ts_cv_2,
    scoring="r2",
    n_iter=100,
    fitted=True,
    verbose=1,
    n_jobs=-1,
)

Fitting 2 folds for each of 100 candidates, totalling 200 fits

---------------------------------------------------------------------------
KeyboardInterrupt                         Traceback (most recent call last)
Cell In[36], line 4
      1 ts_cv_2 = TimeSeriesSplit(
      2     n_splits=2, test_size=test_size, max_train_size=max_train_size, gap=24
      3 )
----> 4 randomized_search_ridge = hgbr_predictions.skb.get_randomized_search(
      5     cv=ts_cv_2,
      6     scoring="r2",
      7     n_iter=100,
      8     fitted=True,
      9     verbose=1,
     10     n_jobs=-1,
     11 )

File ~/work/forecasting/forecasting/.pixi/envs/doc/lib/python3.12/site-packages/skrub/_expressions/_skrub_namespace.py:1736, in SkrubNamespace.get_randomized_search(self, fitted, keep_subsampling, **kwargs)
   1734 if not fitted:
   1735     return search
-> 1736 return search.fit(
   1737     env_with_subsampling(self._expr, self.get_data(), keep_subsampling)
   1738 )

File ~/work/forecasting/forecasting/.pixi/envs/doc/lib/python3.12/site-packages/skrub/_expressions/_estimator.py:682, in ParamSearch.fit(self, environment)
    680     search.param_distributions = param_grid
    681 X, y = _compute_Xy(self.expr, environment)
--> 682 search.fit(X, y)
    683 _copy_attr(search, self, _SKLEARN_SEARCH_FITTED_ATTRIBUTES_TO_COPY)
    684 try:

File ~/work/forecasting/forecasting/.pixi/envs/doc/lib/python3.12/site-packages/sklearn/base.py:1363, in _fit_context.<locals>.decorator.<locals>.wrapper(estimator, *args, **kwargs)
   1356     estimator._validate_params()
   1358 with config_context(
   1359     skip_parameter_validation=(
   1360         prefer_skip_nested_validation or global_skip_validation
   1361     )
   1362 ):
-> 1363     return fit_method(estimator, *args, **kwargs)

File ~/work/forecasting/forecasting/.pixi/envs/doc/lib/python3.12/site-packages/sklearn/model_selection/_search.py:1051, in BaseSearchCV.fit(self, X, y, **params)
   1045     results = self._format_results(
   1046         all_candidate_params, n_splits, all_out, all_more_results
   1047     )
   1049     return results
-> 1051 self._run_search(evaluate_candidates)
   1053 # multimetric is determined here because in the case of a callable
   1054 # self.scoring the return type is only known after calling
   1055 first_test_score = all_out[0]["test_scores"]

File ~/work/forecasting/forecasting/.pixi/envs/doc/lib/python3.12/site-packages/sklearn/model_selection/_search.py:1992, in RandomizedSearchCV._run_search(self, evaluate_candidates)
   1990 def _run_search(self, evaluate_candidates):
   1991     """Search n_iter candidates from param_distributions"""
-> 1992     evaluate_candidates(
   1993         ParameterSampler(
   1994             self.param_distributions, self.n_iter, random_state=self.random_state
   1995         )
   1996     )

File ~/work/forecasting/forecasting/.pixi/envs/doc/lib/python3.12/site-packages/sklearn/model_selection/_search.py:997, in BaseSearchCV.fit.<locals>.evaluate_candidates(candidate_params, cv, more_results)
    989 if self.verbose > 0:
    990     print(
    991         "Fitting {0} folds for each of {1} candidates,"
    992         " totalling {2} fits".format(
    993             n_splits, n_candidates, n_candidates * n_splits
    994         )
    995     )
--> 997 out = parallel(
    998     delayed(_fit_and_score)(
    999         clone(base_estimator),
   1000         X,
   1001         y,
   1002         train=train,
   1003         test=test,
   1004         parameters=parameters,
   1005         split_progress=(split_idx, n_splits),
   1006         candidate_progress=(cand_idx, n_candidates),
   1007         **fit_and_score_kwargs,
   1008     )
   1009     for (cand_idx, parameters), (split_idx, (train, test)) in product(
   1010         enumerate(candidate_params),
   1011         enumerate(cv.split(X, y, **routed_params.splitter.split)),
   1012     )
   1013 )
   1015 if len(out) < 1:
   1016     raise ValueError(
   1017         "No fits were performed. "
   1018         "Was the CV iterator empty? "
   1019         "Were there no candidates?"
   1020     )

File ~/work/forecasting/forecasting/.pixi/envs/doc/lib/python3.12/site-packages/sklearn/utils/parallel.py:82, in Parallel.__call__(self, iterable)
     73 warning_filters = warnings.filters
     74 iterable_with_config_and_warning_filters = (
     75     (
     76         _with_config_and_warning_filters(delayed_func, config, warning_filters),
   (...)     80     for delayed_func, args, kwargs in iterable
     81 )
---> 82 return super().__call__(iterable_with_config_and_warning_filters)

File ~/work/forecasting/forecasting/.pixi/envs/doc/lib/python3.12/site-packages/joblib/parallel.py:2072, in Parallel.__call__(self, iterable)
   2066 # The first item from the output is blank, but it makes the interpreter
   2067 # progress until it enters the Try/Except block of the generator and
   2068 # reaches the first `yield` statement. This starts the asynchronous
   2069 # dispatch of the tasks to the workers.
   2070 next(output)
-> 2072 return output if self.return_generator else list(output)

File ~/work/forecasting/forecasting/.pixi/envs/doc/lib/python3.12/site-packages/joblib/parallel.py:1682, in Parallel._get_outputs(self, iterator, pre_dispatch)
   1679     yield
   1681     with self._backend.retrieval_context():
-> 1682         yield from self._retrieve()
   1684 except GeneratorExit:
   1685     # The generator has been garbage collected before being fully
   1686     # consumed. This aborts the remaining tasks if possible and warn
   1687     # the user if necessary.
   1688     self._exception = True

File ~/work/forecasting/forecasting/.pixi/envs/doc/lib/python3.12/site-packages/joblib/parallel.py:1800, in Parallel._retrieve(self)
   1789 if self.return_ordered:
   1790     # Case ordered: wait for completion (or error) of the next job
   1791     # that have been dispatched and not retrieved yet. If no job
   (...)   1795     # control only have to be done on the amount of time the next
   1796     # dispatched job is pending.
   1797     if (nb_jobs == 0) or (
   1798         self._jobs[0].get_status(timeout=self.timeout) == TASK_PENDING
   1799     ):
-> 1800         time.sleep(0.01)
   1801         continue
   1803 elif nb_jobs == 0:
   1804     # Case unordered: jobs are added to the list of jobs to
   1805     # retrieve `self._jobs` only once completed or in error, which
   (...)   1811     # timeouts before any other dispatched job has completed and
   1812     # been added to `self._jobs` to be retrieved.

KeyboardInterrupt: 

randomized_search_ridge.results_.round(3)

randomized_search_ridge.plot_results().update_layout(margin=dict(l=150))

# nested_cv_results = skrub.cross_validate(
#     environment=predictions.skb.get_data(),
#     pipeline=randomized_search,
#     cv=ts_cv_5,
#     scoring={
#         "r2": get_scorer("r2"),
#         "mape": make_scorer(mean_absolute_percentage_error),
#     },
#     n_jobs=-1,
#     return_pipeline=True,
# ).round(3)
# nested_cv_results

# for outer_fold_idx in range(len(nested_cv_results)):
#     print(
#         nested_cv_results.loc[outer_fold_idx, "pipeline"]
#         .results_.loc[0]
#         .round(3)
#         .to_dict()
#     )

# TODO: Exercise applying a linear model with some additional feature engineering
from sklearn.linear_model import Ridge
from sklearn.kernel_approximation import Nystroem

model = skrub.tabular_learner(
    estimator=Ridge(
        alpha=skrub.choose_float(1e-6, 1e6, log=True, name="alpha", default=1e-3)
    )
)
model.steps.insert(
    -1,
    (
        "nystroem",
        Nystroem(
            n_components=skrub.choose_int(
                10, 200, log=True, name="n_components", default=150
            )
        ),
    ),
)

predictions_ridge = features_with_dropped_cols.skb.apply(model, y=target)
predictions_ridge

altair.Chart(
    pl.concat(
        [
            targets.skb.eval(),
            predictions_ridge.rename(
                {target_column_name: predicted_target_column_name}
            ).skb.eval(),
        ],
        how="horizontal",
    ).tail(24 * 7)
).transform_fold(
    [target_column_name, predicted_target_column_name],
).mark_line(
    tooltip=True
).encode(
    x="prediction_time:T", y="value:Q", color="key:N"
).interactive()

randomized_search_ridge = predictions_ridge.skb.get_randomized_search(
    cv=ts_cv_2,
    scoring="r2",
    n_iter=100,
    fitted=True,
    verbose=1,
    n_jobs=-1,
)

randomized_search_ridge.plot_results().update_layout(margin=dict(l=200))

We observe that the default values of the hyper-parameters are in the optimal region explored by the randomized search. This is a good sign that the model is well-specified and that the hyper-parameters are not too sensitive to small changes of those values.

We could further assess the stability of those optimal hyper-parameters by running a nested cross-validation, where we would perform a randomized search for each fold of the outer cross-validation loop as below but this is computationally expensive.

# nested_cv_results_ridge = skrub.cross_validate(
#     environment=predictions_ridge.skb.get_data(),
#     pipeline=randomized_search_ridge,
#     cv=ts_cv_5,
#     scoring={
#         "r2": get_scorer("r2"),
#         "mape": make_scorer(mean_absolute_percentage_error),
#     },
#     n_jobs=-1,
#     return_pipeline=True,
# ).round(3)

# nested_cv_results_ridge.round(3)

cv_results_ridge = predictions_ridge.skb.cross_validate(
    cv=ts_cv_5,
    scoring={
        "r2": get_scorer("r2"),
        "mape": make_scorer(mean_absolute_percentage_error),
    },
    return_train_score=True,
    return_pipeline=True,
    verbose=1,
    n_jobs=-1,
)

cv_predictions_ridge = collect_cv_predictions(
    cv_results_ridge["pipeline"], ts_cv_5, predictions_ridge, prediction_time
)

plot_lorenz_curve(cv_predictions_ridge, n_samples=500).interactive()

plot_reliability_diagram(cv_predictions_ridge).interactive().properties(
    title="Reliability diagram from cross-validation predictions"
)

from sklearn.multioutput import MultiOutputRegressor

multioutput_predictions = features_with_dropped_cols.skb.apply(
    MultiOutputRegressor(
        estimator=HistGradientBoostingRegressor(random_state=0), n_jobs=-1
    ),
    y=targets.skb.drop(cols=["prediction_time", "load_mw"]).skb.mark_as_y(),
).skb.set_name("multioutput_gbdt")

target_column_names = [target_column_name_pattern.format(horizon=h) for h in horizons]
predicted_target_column_names = [
    f"predicted_{target_column_name}" for target_column_name in target_column_names
]
named_predictions = multioutput_predictions.rename(
    {k: v for k, v in zip(target_column_names, predicted_target_column_names)}
)

import datetime


def plot_horizon_forecast(
    targets, named_predictions, plot_at_time, historical_timedelta
):
    """Plot the true target and the forecast values."""
    merged_data = targets.skb.select(cols=["prediction_time", "load_mw"]).skb.concat(
        [named_predictions], axis=1
    )
    start_time = plot_at_time - historical_timedelta
    end_time = plot_at_time + datetime.timedelta(
        hours=named_predictions.skb.eval().shape[1]
    )
    true_values_past = merged_data.filter(
        pl.col("prediction_time").is_between(start_time, plot_at_time, closed="both")
    ).rename({"load_mw": "Past true load"})
    true_values_future = merged_data.filter(
        pl.col("prediction_time").is_between(plot_at_time, end_time, closed="both")
    ).rename({"load_mw": "Future true load"})
    predicted_record = (
        merged_data.skb.select(
            cols=skrub.selectors.filter_names(str.startswith, "predict")
        )
        .row(by_predicate=pl.col("prediction_time") == plot_at_time, named=True)
        .skb.eval()
    )
    forecast_values = pl.DataFrame(
        {
            "prediction_time": predicted_record["prediction_time"]
            + datetime.timedelta(hours=horizon),
            "Forecast load": predicted_record[
                "predicted_" + target_column_name_pattern.format(horizon=horizon)
            ],
        }
        for horizon in range(1, len(predicted_record))
    )

    true_values_past_chart = (
        altair.Chart(true_values_past.skb.eval())
        .transform_fold(["Past true load"])
        .mark_line(tooltip=True)
        .encode(x="prediction_time:T", y="Past true load:Q", color="key:N")
    )
    true_values_future_chart = (
        altair.Chart(true_values_future.skb.eval())
        .transform_fold(["Future true load"])
        .mark_line(tooltip=True)
        .encode(x="prediction_time:T", y="Future true load:Q", color="key:N")
    )
    forecast_values_chart = (
        altair.Chart(forecast_values)
        .transform_fold(["Forecast load"])
        .mark_line(tooltip=True)
        .encode(x="prediction_time:T", y="Forecast load:Q", color="key:N")
    )
    return (
        true_values_past_chart + true_values_future_chart + forecast_values_chart
    ).interactive()

plot_at_time = datetime.datetime(2025, 5, 24, 0, 0, tzinfo=datetime.timezone.utc)
historical_timedelta = datetime.timedelta(hours=24 * 5)
plot_horizon_forecast(targets, named_predictions, plot_at_time, historical_timedelta)

plot_at_time = datetime.datetime(2025, 5, 25, 0, 0, tzinfo=datetime.timezone.utc)
plot_horizon_forecast(targets, named_predictions, plot_at_time, historical_timedelta)

from sklearn.metrics import r2_score


def multioutput_scorer(regressor, X, y, score_func, score_name):
    y_pred = regressor.predict(X)
    return {
        f"{score_name}_horizon_{h}h": score
        for h, score in enumerate(
            score_func(y, y_pred, multioutput="raw_values"), start=1
        )
    }


def scoring(regressor, X, y):
    return {
        **multioutput_scorer(regressor, X, y, mean_absolute_percentage_error, "mape"),
        **multioutput_scorer(regressor, X, y, r2_score, "r2"),
    }


multioutput_cv_results = multioutput_predictions.skb.cross_validate(
    cv=ts_cv_5,
    scoring=scoring,
    return_train_score=True,
    verbose=1,
    n_jobs=-1,
).round(3)

multioutput_cv_results

import itertools
from IPython.display import display

for metric_name, dataset_type in itertools.product(["mape", "r2"], ["train", "test"]):
    columns = multioutput_cv_results.columns[
        multioutput_cv_results.columns.str.startswith(f"{dataset_type}_{metric_name}")
    ]
    data_to_plot = multioutput_cv_results[columns]
    data_to_plot.columns = [
        col.replace(f"{dataset_type}_", "")
        .replace(f"{metric_name}_", "")
        .replace("_", " ")
        for col in columns
    ]

    data_long = data_to_plot.melt(var_name="horizon", value_name="score")
    chart = (
        altair.Chart(
            data_long,
            title=f"{dataset_type.title()} {metric_name.upper()} Scores by Horizon",
        )
        .mark_boxplot(extent="min-max")
        .encode(
            x=altair.X(
                "horizon:N",
                title="Horizon",
                sort=altair.Sort(
                    [f"horizon {h}h" for h in range(1, data_to_plot.shape[1])]
                ),
            ),
            y=altair.Y("score:Q", title=f"{metric_name.upper()} Score"),
            color=altair.Color("horizon:N", legend=None),
        )
    )

    display(chart)

# TODO: Exercise using RandomForestRegressor
from sklearn.ensemble import RandomForestRegressor

multioutput_predictions_rf = features_with_dropped_cols.skb.apply(
    RandomForestRegressor(min_samples_leaf=30, random_state=0, n_jobs=-1),
    y=targets.skb.drop(cols=["prediction_time", "load_mw"]).skb.mark_as_y(),
).skb.set_name("random_forest")

named_predictions_rf = multioutput_predictions_rf.rename(
    {k: v for k, v in zip(target_column_names, predicted_target_column_names)}
)

plot_at_time = datetime.datetime(2025, 5, 24, 0, 0, tzinfo=datetime.timezone.utc)
historical_timedelta = datetime.timedelta(hours=24 * 5)
plot_horizon_forecast(targets, named_predictions_rf, plot_at_time, historical_timedelta)

plot_at_time = datetime.datetime(2025, 5, 25, 0, 0, tzinfo=datetime.timezone.utc)
plot_horizon_forecast(targets, named_predictions_rf, plot_at_time, historical_timedelta)

multioutput_cv_results_rf = multioutput_predictions_rf.skb.cross_validate(
    cv=ts_cv_5,
    scoring=scoring,
    return_train_score=True,
    verbose=1,
    n_jobs=-1,
)

multioutput_cv_results_rf.round(3)

import itertools
from IPython.display import display

for metric_name, dataset_type in itertools.product(["mape", "r2"], ["train", "test"]):
    columns = multioutput_cv_results_rf.columns[
        multioutput_cv_results.columns.str.startswith(f"{dataset_type}_{metric_name}")
    ]
    data_to_plot = multioutput_cv_results_rf[columns]
    data_to_plot.columns = [
        col.replace(f"{dataset_type}_", "")
        .replace(f"{metric_name}_", "")
        .replace("_", " ")
        for col in columns
    ]

    data_long = data_to_plot.melt(var_name="horizon", value_name="score")
    chart = (
        altair.Chart(
            data_long,
            title=f"{dataset_type.title()} {metric_name.upper()} Scores by Horizon",
        )
        .mark_boxplot(extent="min-max")
        .encode(
            x=altair.X(
                "horizon:N",
                title="Horizon",
                sort=altair.Sort(
                    [f"horizon {h}h" for h in range(1, data_to_plot.shape[1])]
                ),
            ),
            y=altair.Y("score:Q", title=f"{metric_name.upper()} Score"),
            color=altair.Color("horizon:N", legend=None),
        )
    )

    display(chart)

from sklearn.metrics import mean_pinball_loss

scoring = {
    "r2": get_scorer("r2"),
    "mape": make_scorer(mean_absolute_percentage_error),
    "mean_pinball_05_loss": make_scorer(mean_pinball_loss, alpha=0.05),
    "mean_pinball_50_loss": make_scorer(mean_pinball_loss, alpha=0.5),
    "mean_pinball_95_loss": make_scorer(mean_pinball_loss, alpha=0.95),
}

common_params = dict(
    loss="quantile", learning_rate=0.1, max_leaf_nodes=100, random_state=0
)
predictions_gbrt_05 = features_with_dropped_cols.skb.apply(
    HistGradientBoostingRegressor(**common_params, quantile=0.05),
    y=target,
)
predictions_gbrt_50 = features_with_dropped_cols.skb.apply(
    HistGradientBoostingRegressor(**common_params, quantile=0.5),
    y=target,
)
predictions_gbrt_95 = features_with_dropped_cols.skb.apply(
    HistGradientBoostingRegressor(**common_params, quantile=0.95),
    y=target,
)

cv_results_05 = predictions_gbrt_05.skb.cross_validate(
    cv=ts_cv_5,
    scoring=scoring,
    return_pipeline=True,
    verbose=1,
    n_jobs=-1,
)
cv_results_50 = predictions_gbrt_50.skb.cross_validate(
    cv=ts_cv_5,
    scoring=scoring,
    return_pipeline=True,
    verbose=1,
    n_jobs=-1,
)
cv_results_95 = predictions_gbrt_95.skb.cross_validate(
    cv=ts_cv_5,
    scoring=scoring,
    return_pipeline=True,
    verbose=1,
    n_jobs=-1,
)

cv_results_05[[col for col in cv_results_05.columns if col.startswith("test_")]].mean(
    axis=0
).round(3)

cv_results_50[[col for col in cv_results_50.columns if col.startswith("test_")]].mean(
    axis=0
).round(3)

cv_results_95[[col for col in cv_results_95.columns if col.startswith("test_")]].mean(
    axis=0
).round(3)

results = pl.concat(
    [
        targets.skb.select(cols=["prediction_time", target_column_name]).skb.eval(),
        predictions_gbrt_05.rename({target_column_name: "quantile_05"}).skb.eval(),
        predictions_gbrt_50.rename({target_column_name: "median"}).skb.eval(),
        predictions_gbrt_95.rename({target_column_name: "quantile_95"}).skb.eval(),
    ],
    how="horizontal",
).tail(24 * 7)

median_chart = (
    altair.Chart(results)
    .transform_fold([target_column_name, "median"])
    .mark_line(tooltip=True)
    .encode(x="prediction_time:T", y="value:Q", color="key:N")
)

quantile_band_chart = (
    altair.Chart(results)
    .mark_area(opacity=0.4, tooltip=True)
    .encode(
        x="prediction_time:T",
        y="quantile_05:Q",
        y2="quantile_95:Q",
        color=altair.value("lightgreen"),
    )
)

combined_chart = quantile_band_chart + median_chart
combined_chart.interactive()

cv_predictions_05 = collect_cv_predictions(
    cv_results_05["pipeline"], ts_cv_5, predictions_gbrt_05, prediction_time
)
cv_predictions_50 = collect_cv_predictions(
    cv_results_50["pipeline"], ts_cv_5, predictions_gbrt_50, prediction_time
)
cv_predictions_95 = collect_cv_predictions(
    cv_results_95["pipeline"], ts_cv_5, predictions_gbrt_95, prediction_time
)

plot_residuals_vs_predicted(cv_predictions_05).interactive().properties(
    title=(
        "Residuals vs Predicted Values from cross-validation predictions"
        " for quantile 0.05"
    )
)

plot_residuals_vs_predicted(cv_predictions_50).interactive().properties(
    title=(
        "Residuals vs Predicted Values from cross-validation predictions" " for median"
    )
)

plot_residuals_vs_predicted(cv_predictions_95).interactive().properties(
    title=(
        "Residuals vs Predicted Values from cross-validation predictions"
        " for quantile 0.95"
    )
)

cv_predictions_05_concat = pl.concat(cv_predictions_05, how="vertical")
cv_predictions_50_concat = pl.concat(cv_predictions_50, how="vertical")
cv_predictions_95_concat = pl.concat(cv_predictions_95, how="vertical")

import matplotlib.pyplot as plt
from sklearn.metrics import PredictionErrorDisplay


for kind in ["actual_vs_predicted", "residual_vs_predicted"]:
    fig, axs = plt.subplots(1, 3, figsize=(15, 5), sharey=True)

    PredictionErrorDisplay.from_predictions(
        y_true=cv_predictions_05_concat["load_mw"].to_numpy(),
        y_pred=cv_predictions_05_concat["predicted_load_mw"].to_numpy(),
        kind=kind,
        ax=axs[0],
    )
    axs[0].set_title("0.05 quantile regression")

    PredictionErrorDisplay.from_predictions(
        y_true=cv_predictions_50_concat["load_mw"].to_numpy(),
        y_pred=cv_predictions_50_concat["predicted_load_mw"].to_numpy(),
        kind=kind,
        ax=axs[1],
    )
    axs[1].set_title("Median regression")

    PredictionErrorDisplay.from_predictions(
        y_true=cv_predictions_95_concat["load_mw"].to_numpy(),
        y_pred=cv_predictions_95_concat["predicted_load_mw"].to_numpy(),
        kind=kind,
        ax=axs[2],
    )
    axs[2].set_title("0.95 quantile regression")

    fig.suptitle(f"{kind} for GBRT minimzing different quantile losses")

def coverage(y_true, y_quantile_low, y_quantile_high):
    y_true = np.asarray(y_true)
    y_quantile_low = np.asarray(y_quantile_low)
    y_quantile_high = np.asarray(y_quantile_high)
    return float(
        np.logical_and(y_true >= y_quantile_low, y_true <= y_quantile_high)
        .mean()
        .round(4)
    )


def mean_width(y_true, y_quantile_low, y_quantile_high):
    y_true = np.asarray(y_true)
    y_quantile_low = np.asarray(y_quantile_low)
    y_quantile_high = np.asarray(y_quantile_high)
    return float(np.abs(y_quantile_high - y_quantile_low).mean().round(1))


def binned_coverage(y_true_folds, y_quantile_low, y_quantile_high, n_bins=10):
    """Compute coverage after binning true values using quantile-based binning.

    Parameters
    ----------
    y_true_folds : list of numpy.ndarray
        List of true target values, one array per CV fold
    y_quantile_low : list of numpy.ndarray
        List of lower quantile predictions, one array per CV fold
    y_quantile_high : list of numpy.ndarray
        List of upper quantile predictions, one array per CV fold
    n_bins : int, default=10
        Number of bins to create

    Returns
    -------
    pandas.DataFrame
        DataFrame with columns: bin_left, bin_right, bin_center, fold_idx,
        coverage, mean_width, n_samples
    """
    # Use all true values to define global bin boundaries
    all_true_values = np.concatenate(y_true_folds)
    df = pd.DataFrame({"bin_by": all_true_values})
    df["bin"] = pd.qcut(df["bin_by"], q=n_bins, labels=False, duplicates="drop")

    # Get bin boundaries for consistent binning across folds
    bin_boundaries = []
    for bin_idx in sorted(df["bin"].dropna().unique()):
        bin_mask = df["bin"] == bin_idx
        bin_values = df.loc[bin_mask, "bin_by"]
        bin_boundaries.append((bin_values.min(), bin_values.max()))

    results = []
    n_folds = len(y_quantile_low)

    for fold_idx in range(n_folds):
        fold_true = y_true_folds[fold_idx]
        fold_low = y_quantile_low[fold_idx]
        fold_high = y_quantile_high[fold_idx]

        # Assign each sample in this fold to a bin
        fold_bins = (
            np.digitize(fold_true, bins=[b[0] for b in bin_boundaries] + [np.inf]) - 1
        )

        for bin_idx, (bin_left, bin_right) in enumerate(bin_boundaries):
            # Get samples from this fold that fall into this bin
            bin_mask = fold_bins == bin_idx

            if np.sum(bin_mask) == 0:
                # No samples in this bin for this fold
                continue

            fold_bin_true = fold_true[bin_mask]
            fold_bin_low = fold_low[bin_mask]
            fold_bin_high = fold_high[bin_mask]

            bin_center = (bin_left + bin_right) / 2
            n_samples_in_bin = len(fold_bin_true)

            coverage_score = coverage(fold_bin_true, fold_bin_low, fold_bin_high)
            width = mean_width(fold_bin_true, fold_bin_low, fold_bin_high)

            results.append(
                {
                    "bin_left": bin_left,
                    "bin_right": bin_right,
                    "bin_center": bin_center,
                    "fold_idx": fold_idx,
                    "coverage": coverage_score,
                    "mean_width": width,
                    "n_samples": n_samples_in_bin,
                }
            )

    return pd.DataFrame(results)

coverage(
    cv_predictions_50_concat["load_mw"].to_numpy(),
    cv_predictions_05_concat["predicted_load_mw"].to_numpy(),
    cv_predictions_95_concat["predicted_load_mw"].to_numpy(),
)

mean_width(
    cv_predictions_50_concat["load_mw"].to_numpy(),
    cv_predictions_05_concat["predicted_load_mw"].to_numpy(),
    cv_predictions_95_concat["predicted_load_mw"].to_numpy(),
)

# Compute binned coverage scores
binned_coverage_results = binned_coverage(
    [df["load_mw"].to_numpy() for df in cv_predictions_50],
    [df["predicted_load_mw"].to_numpy() for df in cv_predictions_05],
    [df["predicted_load_mw"].to_numpy() for df in cv_predictions_95],
    n_bins=10,
)

binned_coverage_results

coverage_by_bin = binned_coverage_results.copy()
coverage_by_bin["bin_label"] = coverage_by_bin.apply(
    lambda row: f"[{row.bin_left:.0f}, {row.bin_right:.0f}]", axis=1
)

Reliability diagram for quantile regression

plot_reliability_diagram(
    cv_predictions_50, kind="quantile", quantile_level=0.50
).interactive().properties(
    title="Reliability diagram for quantile 0.50 from cross-validation predictions"
)

plot_reliability_diagram(
    cv_predictions_05, kind="quantile", quantile_level=0.05
).interactive().properties(
    title="Reliability diagram for quantile 0.05 from cross-validation predictions"
)

plot_reliability_diagram(
    cv_predictions_95, kind="quantile", quantile_level=0.95
).interactive().properties(
    title="Reliability diagram for quantile 0.95 from cross-validation predictions"
)

ax = coverage_by_bin.boxplot(
    column="coverage", by="bin_label", figsize=(12, 6), vert=False, whis=1000
)
ax.axvline(x=0.9, color="red", linestyle="--", label="Target coverage (0.9)")
ax.set_xlabel("Load bins (MW)")
ax.set_ylabel("Coverage")
ax.set_title("Coverage Distribution by Load Bins")
ax.legend()
plt.suptitle("")  # Remove automatic suptitle from boxplot
plt.xticks(rotation=45)
plt.tight_layout()

Quantile regression as classification

In the following, we turn a quantile regression problem for all possible quantile levels into a multiclass classification problem by discretizing the target variable into bins and interpolating the cumulative sum of the bin membership probability to estimate the CDF of the distribution of the continuous target variable conditioned on the features.

Ideally, the classifier should be efficient when trained on a large number of classes (induced by the number of bins). Therefore we use a Random Forest classifier as the default base estimator.

from scipy.interpolate import interp1d
from sklearn.base import BaseEstimator, RegressorMixin, clone
from sklearn.utils.validation import check_is_fitted
from sklearn.ensemble import RandomForestClassifier
from sklearn.preprocessing import KBinsDiscretizer
from sklearn.utils.validation import check_consistent_length
from sklearn.utils import check_random_state
import numpy as np


class BinnedQuantileRegressor(BaseEstimator, RegressorMixin):
    def __init__(
        self,
        estimator=None,
        n_bins=100,
        quantile=0.5,
        random_state=None,
    ):
        self.n_bins = n_bins
        self.estimator = estimator
        self.quantile = quantile
        self.random_state = random_state

    def fit(self, X, y):
        # Lightweight input validation: most of the input validation will be
        # handled by the sub estimators.
        random_state = check_random_state(self.random_state)
        check_consistent_length(X, y)
        self.target_binner_ = KBinsDiscretizer(
            n_bins=self.n_bins,
            strategy="quantile",
            subsample=200_000,
            encode="ordinal",
            random_state=random_state,
        )

        y_binned = (
            self.target_binner_.fit_transform(np.asarray(y).reshape(-1, 1))
            .ravel()
            .astype(np.int32)
        )

        # Fit the multiclass classifier to predict the binned targets from the
        # training set.
        if self.estimator is None:
            estimator = RandomForestClassifier(random_state=random_state)
        else:
            estimator = clone(self.estimator)
        self.estimator_ = estimator.fit(X, y_binned)
        return self

    def predict_quantiles(self, X, quantiles=(0.05, 0.5, 0.95)):
        check_is_fitted(self, "estimator_")
        edges = self.target_binner_.bin_edges_[0]
        n_bins = edges.shape[0] - 1
        expected_shape = (X.shape[0], n_bins)
        y_proba_raw = self.estimator_.predict_proba(X)

        # Some might stay empty on the training set. Typically, classifiers do
        # not learn to predict an explicit 0 probability for unobserved classes
        # so we have to post process their output:
        if y_proba_raw.shape != expected_shape:
            y_proba = np.zeros(shape=expected_shape)
            y_proba[:, self.estimator_.classes_] = y_proba_raw
        else:
            y_proba = y_proba_raw

        # Build the mapper for inverse CDF mapping, from cumulated
        # probabilities to continuous prediction.
        y_cdf = np.zeros(shape=(X.shape[0], edges.shape[0]))
        y_cdf[:, 1:] = np.cumsum(y_proba, axis=1)
        return np.asarray([interp1d(y_cdf_i, edges)(quantiles) for y_cdf_i in y_cdf])

    def predict(self, X):
        return self.predict_quantiles(X, self.quantile).ravel()